entails another proposition , we have the feeling that either
of the following two things is going on. The content of

is identical to, or a part of, the
content of

; the proposition expresses the reality which is identical to, or a proper part
of, the reality that the proposition

expresses. For example,

entails , the truthmaker for

can be a truthmaker for
. Firstly, if the contents of

and are exactly the same, what makes one true should
also make the other proposition true. Secondly, if the content of

is only a part of the
content of

, then whatever makes

true should also make true. This is clear from
the example used in the above. If some truthmaker makes

and have the same truthmaker if they both express the same reality
in different ways. For instance,

expresses only a part of the
reality that

expresses, it seems that the truthmaker for

can also be a truthmaker for
. Suppose there is a reality such that three objects, a knife, a fork and a spoon, are lined
up from right to left in that order. Then, this reality is the truthmaker for the proposition

true, also makes another proposition
true if

entails . Following Armstrong's symbolization more or less, the principle can
be represented as:
1. T

2.

entails
XC3. T

;CqFԍSee Armstrong 2004, 10.;,WCGqF_ԍI use `T

' to mean T is a truthmaker for

.W
X{a/3. Negative Factsă
Russell thought that negative truths are made true by the special type of facts, negative
facts, but he did not investigate the structure of these special facts (1985, sec. III). So, we
shall take up where Russell left off and try to come up with the logical form of negative facts
here. In doing this, we will assume two things: that the only elements that constitute the world
are particulars, properties, relations, and facts; that negative facts are distinct from positive
facts which make positive truths true.
We might think that what makes negative facts distinct from positive facts is that they have
negative particulars in their constituents, where negative particulars are the counterparts of
regular particulars such that the presence of them in the facts make negative propositions true.
So, the logical form of negative facts is negative particulars having positive properties or
being related to one another by positive relations. To illustrate, suppose that

, is true>, where <~p> is a description of in the
sense that <~p> does not directly refer to any particular state of affairs. We may describe

by <~p> because

is related to a number of propositions by the incompatibility relation
and one of the propositions that

is so related is

. Furthermore, since <~p> is another
way of saying , the truthmaker for <~p> is the truthmaker for

.
For instance, take the negative proposition,

is true when the two constituent propositions,

and , are both true. Further, the condition
for the truth of these two propositions is that they each have their respective truthmakers (i.e.,
T1 for

and T2 for are both true, the condition for being both true is that ). Now, consider, <~p>. <~p> is true when

.P
qF
ԍI am using `|' as the Sheffer stroke symbol.P
Regarding

, we can say the following things:

is true when

and

and

is true and

is false, and what makes true and

false is the truthmaker for and the
falsemaker for

. Since the falsemaker for

is the truthmaker for <~p>, the truthmaker
for and the truthmaker for <~p>. It follows that the truthmaker for

by
itself is not sufficient to make

and with

and for <~p>. However,

and for <~p>. This is clearly intolerable. For this reason, the
incompatibility solution should be abandoned and the truthmaker for <~p> should be thought
to be simply the negative fact for <~p>.
Our response to this objection on behalf of the incompatibilits is that the objection seems
to make an unwarranted assumption. The objection unwarrantedly assumes that the condition
for the truth of

is that

is true and

is false, and it concludes that what
makes true is the sum of the truthmaker for

and the falsemaker for

(i.e.
negative fact that <~p>). However, the incompatibilists can just say that the condition for is true, and that the falsehood of 's being true is that

is true and

is
a consequence of the truth of . Thus, from the incompatibilists' point of view,
what makes , rather than the sum of the truthmaker for and

true is the sum of the truthmaker for

and the truthmaker for

and the falsemaker for

.
From what has been said in response to the objection we have considered, however, we#b}
p-++!!ought to finetune our view of the truthmaker for the negative truth (i.e., < : < together imply : together imply (i.e.,

(i.e.,

:

and

:

and